Macroscopic description of porous media is based on two basic assumptions: continuous medium approximation, which disregards microscopic structure of the material and assumes continuous distribution of the matter in space, and phenomenological response coefficient approximation, which disregards internal degrees of freedom of the material and assumes that the material responds to the external force (temperature or pressure gradient, electric potential, etc.) as an unstructured entity with certain response coefficient (thermal conductivity, permeability, electric conductivity, etc.)
Since macroscopic modeling is a primary tool in many industrial and scientific applications, the microscopic modeling is often considered an auxiliary tool for estimating the macroscopic response coefficients.
Yet there is a lot of experimental data indicating that the macroscopic models are insufficient.
For the first example, one-phase macroscopic fluid transport model is based on permeability coefficient. It is well known, that a rather extensive set of one-phase transport phenomena lies outside the permeability coefficient concept (thermocapillary, osmotic, Graham, Klinkenberg and other effects).
For the second example, multiphase fluid transport model is based on phase permeability coefficients. Many observed transport phenomena indicate, that this approach is insufficient and microscopic processes are important (hysteresis of phase permeabilities, cross-term effects, film lubrication effects, capillary number influence, etc.).
U.S. Pat. No. 6,516,080 describes a numerical method of estimating a desired physical property of a three-dimensional porous medium, said desired physical property being selected from the group consisting of fluid flow properties, electrical properties, elastic properties, permeability, electrical conductivity, and elastic wave velocity. According to this method a three-dimensional model is reconstructed from experimental two-dimensional images by statistical means; properties are calculated using a numerical solver of Navier-Stokes equations, or a Lattice-Boltzmann flow simulator, or any finite element numerical solver.
The limitations of this patent are following: patent is focused on acquisition of macroscopic properties without validation of these properties; possible multiphase and thermal effects are not mentioned; possible non-newtonian rheology of fluids is not mentioned; possible phase transitions fluid-fluid (like gas-condensate) and fluid-solid (like wax deposition from oil, salt deposition from water solution) are not mentioned; possible surfactant effects (like change of wettability or interfacial tension) are not mentioned; possible geochemical effects (like clay imbibition) are not mentioned; possible chemical reactions are not mentioned.
These examples demonstrate that there are many phenomena, which significantly influence transport through saturated porous solid; and one cannot apriori be sure that under realistic conditions the considered material can be adequately described by some standard macroscopic continuous medium model. The microscopic model can provide a lot of information outside macroscopic description. It can either validate the macroscopic model, or show its limitations, or even show its inapplicability.
The modern computation facilities provide the possibility to use micromodels of porous solids directly for the calculation of heat, mass, chemical and electric fluxes under given external conditions. This data can be generalized by statistical means for the large-scale transport modeling.